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ERIC Number: EJ992768
Record Type: Journal
Publication Date: 2012-Nov
Pages: 27
Abstractor: As Provided
ISBN: N/A
ISSN: ISSN-0021-8251
The Splitting Group
Norton, Anderson; Wilkins, Jesse L. M.
Journal for Research in Mathematics Education, v43 n5 p557-583 Nov 2012
Piagetian theory describes mathematical development as the construction and organization of mental operations within psychological structures. Research on student learning has identified the vital roles of two particular operations--splitting and units coordination--play in students' development of advanced fractions knowledge. Whereas Steffe and colleagues (e.g., Steffe, 2001; Steffe & Olive, 2010) describe these knowledge structures in terms of fractions schemes, Piaget introduced the possibility of modeling students' psychological structures with formal mathematical structures, such as algebraic groups. This paper demonstrates the utility of modeling students' development with a structure that is isomorphic to the positive rational numbers under multiplication--the "splitting group." We use a quantitative analysis of written assessments from 58 eighth grade students to test hypotheses related to this development. Results affirm and refine an existing hypothetical learning trajectory for students' constructions of advanced fractions schemes by demonstrating that splitting is a necessary precursor to students' constructions of 3 levels of units coordination. (Contains 10 figures, 8 tables and 10 footnotes.)
National Council of Teachers of Mathematics. 1906 Association Drive, Reston, VA 20191-1502. Tel: 800-235-7566; Tel: 703-620-3702; Fax: 703-476-2970; e-mail: orders@nctm.org; Web site: http://www.nctm.org/publications/
Publication Type: Journal Articles; Reports - Research
Education Level: Grade 8
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A